DISTANCE COMPUTING FORM — ANDOYER-LAMBERT 



TYPE APPROXIMATION WITH SECOND ORDER TERMS 



(No conversion to parametric latitudes) 



Clarke Spheroid 1866, a = 6,378,206.4 meters 



f/2 = 0.00169503765, f/4 = 0.000847518825, f7l28 = 0.0897860195 x 10"' 



O 1 11 O I M . 



Jn cf,, -f-' /'PJ -S-^JS-^-^ 2. west of 1. AA = A,-A^ • ^ J^ ^^,/^^ 



cos ch, -r^ ff'/fyi^^^ sin ^S, t./'^J <^'/f'^f ^\n K\ -T.^^^" ^^^^S^T ^ 



tan ^^ 7"^ ^^^ .^<^ j^-P'V cos <^, X^ /j^^/'^^^x^' ^os AA ?^^ ^^^ .^ ^^^i^ 



tan 0; "^ ^ / ^<^ cf«^<^ ^iT cos j = gin 0, sin ijS^ + cos 0^ cos c/S^ cos A A 7^^ ^^^ ^ P/^0 ^ 



M = cos 0, tan <^, - sin 4,, cos AA f, ^<^^ W/\S :i^ ^^^ „ ^ [^/gj„ ^^ ?". ^^/ V<^^9< i, 

 N = cos <^, tan 4>,- sin <^, cos AA - . ^^^ ^^^ vf ,/^ ,„, ^ ^j/^i^ ^;, - , ^^^ ^/^f ^ 

 sin d = cos ^,sinAA/sin v = cos ^S^sin AA /sin „ T'<^3ir^.;i^</.^^ ^^ jf f </</ ^9. '/^ 'P' 



CSC d ^^f' ^^"^ ^^^ ^ cot d r^^' ^^f^y ^^ V >^^ ^^^s^^^ o 



1 + cc.^^ -^z-^ff^f/'^^ 1-cos d v. <i'^<:? <y/^;?3 sin u ■^' fff y9^^'/ 



(.in ^, + sin A..y ~^./J?£)^^^/A (snn r/.,-sin ^J ^ -j'-^ / / /^ "" ^ sin V y-/- ^^^ 0£^ C <? <0 



Kl = (sin<^. + sin(^,)^/(l + COS d V/> ^«g^.^ ^;'<^ry.J .k-^ = (sin rA,-sin rA,^Vfl-ros d) ^' '^J^/?^ //^ ^ 



y^ y> ^'^>^C3£, 9f/9^ ^ ^-^.£>aS^Sy6 ?^yL7 d 7^^.^jr>^ ^/^J? A d.^ r?^^ ^^^.^.^^sT^J^.^^ .^ 

 A = 64d^ + 16d^cot d /-J>- ^//-?>^ "/^^g^ J' n ° 48'sin d +8d; esc d ?^X V/Ji- <7J(S9^ ^ 

 B = -9n —?..^.^5Vy^:^// F - 30 sin 2d t/.^f/S /^^^ sin 2d ■>^^ ^6'^ VS ^ f "/ 

 C= -(30i. +8d^ n.^ ^4F/9^ -/ 9/<r-^^^^^ AX ^^. /^/ 7/^-<^VS 



RY — y^^^f^^s''? rv^ ~,^^^J3rX// nxY -r.c^^/S^S f/^ 9 



PY . :/-, ^^^r^'ffs'f/ a. ^, = AX + RY + ry^ + nxY+F.Y^ ^. ^'/^J2::>^ ^4-^ 



;id^^-/fMuv^^-w.;n^ v>*^^<r^^v/^^y/^' fdj^ =+(fvi28is -J> ^^x^-^ y/^ -/ 



d^ + ;;d^ 7^^^^^'-=gs?/<^ F'^^^ d^ + Sdf + ;^H^^ 7-> ^^<S-JS/C 9s-S^ 



S(5dp = a(d^ + f.A y^^.^^'^- 9f? S(5dp) = a(d^ + Sdf + gdp) /4^, ^JU ' ^^^ ^ ^ 



T ^ d/sin d y-/ ^^^ /^6-9:^^ ^ 

 2u ^^^^ <^^ yT/>>/y 2v Xi^P c?^::; <^ci.yJ^<^ 



sin 2v —.<^^'^ <P^9C.^ 

 y =(f/2) cosy, sin 1^1 —V- ^9f / /^' 2_^ 



TTT ^ /> v<^ ^ov y /^ -^ ^ 



= -UT + V -/- y^^^YX^ ~^ 

 + Sv^r ^^^^^9 



9^ cy<^ <^^.<^<^<:^ 



sin 



2ii '9-'' 



^^^f 



^»?^ -2- 



TT = 



(f/2)cos'<?!)isin 2uJ 



^X 4f^ J^JV^V<J7 — ^ 



A^T 



/^- ^ 



i^n 



= VT-U: 



^/,^-7^JL )( /^ -^^ 



+ ^1 





^<?. <J'^^ 





f9 



v/ 



vff, ^s5'^ 



a, . 



+180 



9^ 







xr^ /^. i^^ 



+ V 



+180 o . M 



■x^^ = 180°- u + 8xx a^_, = flvu = ^^°° + V + Sv 

 Line No. 2, See Tables 1 and 2. True distance /^^ f3^ J 9^ ^ 



127 



